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Dependence of events, revisited

Published online by Cambridge University Press:  23 August 2024

Peter Braza
Peter Braza*
Affiliation:
University of Colorado, Colorado Springs, 1420 Austin Bluffs Road, Colorado Springs, CO 80918 USA e-mail: [email protected]
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Independence is a key concept in probability. Conceptually, we think of two events as being independent if the outcome of one event doesn’t affect the outcome of the other and vice versa. Mathematically, we say that events A and B are independent if the probability that both occur is the product of the probabilities that each occurs. More precisely, P (A ∩ B) = P (A) (P (B) in which P () denotes the probability of the given event. Alternatively, we say that A and B are independent if the conditional probability that A occurs given that B has occurred, P (A | B), satisfies P (A | B) = P (A). That is, whether or not B occurs does not affect whether or not A occurs.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 572 , July 2024 , pp. 257 - 261
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

Rényi, A., On measures of dependence, Acta Math. Acad. Sci. Hungary. 10, pp. 441–451 (1959).CrossRefGoogle Scholar
Li, Hui, A true measure of dependence, Munich Personal RePEc Archive (2016), available at https://mpra.ub.uni-muenchen.de/69735/ Google Scholar
Czeslaw, Stepniak, A note on correlation coefficient between random events, Discussiones Mathematicae, Probability and Statistics, 35 pp 57–60 (2015).Google Scholar
Kubik, L.T., Probability, A textbook for teaching mathematics studies (in Polish), Polish Scientific Publishers (1980).Google Scholar
Pitman, Jim, Probability, Springer-Verlag (1993).CrossRefGoogle Scholar
Ross, Sheldon, A first course in probability, Collier Macmillan (1976).Google Scholar
DeGroot, Morris H., Probability and statistics, Addison-Wesley (1975).Google Scholar